Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{6} + 5x^{4} + 6x^{2} + 1 \)
| $\times$ | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 15, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 28 }(1, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 15, ·)\) |
| \(\chi_{ 28 }(25, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 11, ·)\) |
| \(\chi_{ 28 }(23, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 9, ·)\) |
| \(\chi_{ 28 }(9, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 23, ·)\) |
| \(\chi_{ 28 }(11, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 25, ·)\) |
| \(\chi_{ 28 }(15, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 1, ·)\) |